Reproduction of river meander cutoffs in laboratory has been found to be a challenging endeavor. In particular, stream bank failure is difficult to reproduce at small laboratory scales. Even though it may be much simpler to balance bank erosion and bank accretion with the help of numerical models, the difficulties to numerically model cutoffs remain. Existing numerical models for meander migration frequently tend to treat cutoffs as a fleet process. In this study, two distinctive but inter-related methods to model cutoffs are discussed. Both methods solve the 2D depth-averaged, unsteady Reynolds-averaged Navier–Stokes equations (URANS) coupled with k-ε model for turbulence closure. The Meyer-Peter Müller formula with the Exner equation are solved for bedload transport and bed morphology evolution. In the first method, the cutoff starts to develop through a process that periodically widens the chute cutoff channel. After each widening event, an originally non-erodible portion of floodplain collapses and becomes erodible. The coupling period of the widening process is subject to calibration. In the second method, the widening process is simulated with a hybrid deterministic-stochastic bank failure model. The widening process in this method is governed by the near bank sheer stress and the bank critical shear stress. The method assumes Gaussian distributions of both near bank shear stress and critical bank shear stress to evaluate the bank failure risk. Both methods are tested using a simplified bench scale chute cutoff, which is scaled down from a natural chute cutoff in the Wabash River, between Illinois and Indiana, USA.